Document Open Access Logo

Is This Correct? Let’s Check!

Authors Omri Ben-Eliezer , Dan Mikulincer , Elchanan Mossel , Madhu Sudan

Thumbnail PDF


  • Filesize: 0.65 MB
  • 11 pages

Document Identifiers

Author Details

Omri Ben-Eliezer
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Dan Mikulincer
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Elchanan Mossel
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Madhu Sudan
  • School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

Cite AsGet BibTex

Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel, and Madhu Sudan. Is This Correct? Let’s Check!. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 15:1-15:11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


Societal accumulation of knowledge is a complex process. The correctness of new units of knowledge depends not only on the correctness of new reasoning, but also on the correctness of old units that the new one builds on. The errors in such accumulation processes are often remedied by error correction and detection heuristics. Motivating examples include the scientific process based on scientific publications, and software development based on libraries of code. Natural processes that aim to keep errors under control, such as peer review in scientific publications, and testing and debugging in software development, would typically check existing pieces of knowledge - both for the reasoning that generated them and the previous facts they rely on. In this work, we present a simple process that models such accumulation of knowledge and study the persistence (or lack thereof) of errors. We consider a simple probabilistic model for the generation of new units of knowledge based on the preferential attachment growth model, which additionally allows for errors. Furthermore, the process includes checks aimed at catching these errors. We investigate when effects of errors persist forever in the system (with positive probability) and when they get rooted out completely by the checking process. The two basic parameters associated with the checking process are the probability of conducting a check and the depth of the check. We show that errors are rooted out if checks are sufficiently frequent and sufficiently deep. In contrast, shallow or infrequent checks are insufficient to root out errors.

Subject Classification

ACM Subject Classification
  • Networks → Error detection and error correction
  • Error Propagation
  • Preferential Attachment


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. David B Allison, Richard M Shiffrin, and Victoria Stodden. Reproducibility of research: Issues and proposed remedies. Proceedings of the National Academy of Sciences, 115(11):2561-2562, 2018. Google Scholar
  2. Noga Alon, Elchanan Mossel, and Robin Pemantle. Distributed Corruption Detection in Networks. Theory of Computing, 16(1):1-23, 2020. Google Scholar
  3. Omri Ben-Eliezer, Elchanan Mossel, and Madhu Sudan. Information spread with error correction. CoRR, abs/2107.06362, 2021. URL:
  4. William S. Evans and Leonard J. Schulman. Signal propagation and noisy circuits. IEEE Trans. Inform. Theory, 45(7):2367-2373, 1999. Google Scholar
  5. Lawrence F. Gray. A reader’s guide to Gacs’s “positive rates” paper. Journal of Statistical Physics, 103(1):1-44, 2001. Google Scholar
  6. Joseph F. Grcar. Errors and corrections in mathematics literature. Notices of the AMS, 60(4):418-425, 2013. Google Scholar
  7. John P. A. Ioannidis. Why most published research findings are false. PLOS Medicine, 2(8), 2005. Google Scholar
  8. John P. A. Ioannidis. Why science is not necessarily self-correcting. Perspectives on Psychological Science, 7(6):645-654, 2012. Google Scholar
  9. Piers Larcombe and Peter Ridd. The need for a formalised system of quality control for environmental policy-science. Marine Pollution Bulletin, 126:449-461, 2018. Google Scholar
  10. Helen Longino. The Social Dimensions of Scientific Knowledge. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Summer 2019 edition, 2019. Google Scholar
  11. Anuran Makur, Elchanan Mossel, and Yury Polyanskiy. Broadcasting on random directed acyclic graphs. IEEE Transactions on Information Theory, 66(2):780-812, 2020. Google Scholar
  12. Charles Piller. Blots on a field. Science, 377(6604):358-363, 2022. Google Scholar
  13. Franco P. Preparata, Gernot Metze, and Robert T. Chien. On the connection assignment problem of diagnosable systems. IEEE Transactions on Electronic Computers, 6(EC-16):848-854, 1967. Google Scholar
  14. Dennis Selkoe and Jeffrey Cummings. News story miscasts Alzheimer’s science. Science, 377(6609):934-935, 2022. Google Scholar
  15. John von Neumann. Probabilistic logics and the synthesis of reliable organisms from unreliable components. In Automata studies, Annals of mathematics studies, no. 34, pages 43-98. Princeton University Press, Princeton, N. J., 1956. Google Scholar
  16. George Udny Yule. A mathematical theory of evolution, based on the conclusions of Dr. JC Willis, FR S. Philosophical transactions of the Royal Society of London. Series B, containing papers of a biological character, 213(402-410):21-87, 1925. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail